Over-the-Counter Monograph Safety, Innovation, and Reform Act of 2019 This bill makes significant changes to the regulation by the Food and Drug Administration (FDA) of nonprescription (i.e., over-the-counter or OTC) drugs. The bill establishes a new approval process for OTC medications. Specifically, it creates an FDA administrative order process for the evaluation of OTC products, replacing the present notice and comment rulemaking approach. Under the new process, the FDA may issue an administrative order determining that a specific OTC drug, class of drugs, or combination is generally regarded as safe and effective and not subject to the new drug application process. The FDA may also use the administrative order process to (1) determine that a drug, class of drugs, or combination poses an imminent hazard to the public health; or (2) require labeling changes to mitigate a significant or unreasonable risk of a serious adverse event associated with use of the drug. The bill provides for market exclusivity under certain circumstances. For drugs determined to be generally regarded as safe and effective pursuant to an administrative order requested by a sponsor (rather than initiated by the FDA), the requestor is granted 18 months of market exclusivity. This market exclusivity applies to an OTC drug with a new active ingredient or if the requestor conducted new human studies to get approval. The bill allows a sponsor of a nonprescription sunscreen active ingredient or a combination of such ingredients that was subject to a proposed sunscreen order to transition to the administrative order process. Market exclusivity provisions also apply to new sunscreen active ingredients. The FDA must establish a user fee program for OTC drugs.